{"id":"https://openalex.org/W3147466994","doi":"https://doi.org/10.1007/s10589-022-00369-9","title":"Second order semi-smooth Proximal Newton methods in Hilbert spaces","display_name":"Second order semi-smooth Proximal Newton methods in Hilbert spaces","publication_year":2022,"publication_date":"2022-04-09","ids":{"openalex":"https://openalex.org/W3147466994","doi":"https://doi.org/10.1007/s10589-022-00369-9","mag":"3147466994"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-022-00369-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-022-00369-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00369-9.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00369-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059737468","display_name":"Bastian P\u00f6tzl","orcid":"https://orcid.org/0000-0002-3578-6424"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bastian P\u00f6tzl","raw_affiliation_strings":["Chair of Applied Mathematics, University of Bayreuth, Universit\u00e4tsstra\u00dfe 30, 95440, Bayreuth, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3578-6424","affiliations":[{"raw_affiliation_string":"Chair of Applied Mathematics, University of Bayreuth, Universit\u00e4tsstra\u00dfe 30, 95440, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040824080","display_name":"Anton Schiela","orcid":"https://orcid.org/0000-0002-6959-2951"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anton Schiela","raw_affiliation_strings":["Chair of Applied Mathematics, University of Bayreuth, Universittsstrae 30, 95440 Bayreuth, Germany","Chair of Applied Mathematics, University of Bayreuth, Universit\u00e4tsstra\u00dfe 30, 95440, Bayreuth, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Applied Mathematics, University of Bayreuth, Universittsstrae 30, 95440 Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]},{"raw_affiliation_string":"Chair of Applied Mathematics, University of Bayreuth, Universit\u00e4tsstra\u00dfe 30, 95440, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036333354","display_name":"Patrick Jaap","orcid":"https://orcid.org/0000-0001-8567-9988"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Patrick Jaap","raw_affiliation_strings":["Institut fr Numerische Mathematik, Technische Universitt Dresden, Zellescher Weg 12-14, 01069 Dresden, Germany","Institut f\u00fcr Numerische Mathematik, Technische Universit\u00e4t Dresden, Zellescher Weg 12-14, 01069, Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut fr Numerische Mathematik, Technische Universitt Dresden, Zellescher Weg 12-14, 01069 Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]},{"raw_affiliation_string":"Institut f\u00fcr Numerische Mathematik, Technische Universit\u00e4t Dresden, Zellescher Weg 12-14, 01069, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059737468"],"corresponding_institution_ids":["https://openalex.org/I54009628"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6405,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58123009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"82","issue":"2","first_page":"465","last_page":"498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8165621161460876},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7157017588615417},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6756271123886108},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6706603169441223},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6420567035675049},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5426954627037048},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5262664556503296},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5126006007194519},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5021908283233643},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47103315591812134},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.460224449634552},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4481040835380554},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.44400981068611145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43063411116600037},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41693204641342163},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.37219473719596863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13623547554016113},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0896262526512146},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08555760979652405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165621161460876},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7157017588615417},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6756271123886108},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6706603169441223},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6420567035675049},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5426954627037048},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5262664556503296},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5126006007194519},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5021908283233643},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47103315591812134},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.460224449634552},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4481040835380554},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.44400981068611145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43063411116600037},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41693204641342163},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37219473719596863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13623547554016113},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0896262526512146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08555760979652405},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10589-022-00369-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-022-00369-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00369-9.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:epub.uni-bayreuth.de:6731","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400362","display_name":"EPub Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"},{"id":"pmh:oai:RePEc:spr:coopap:v:82:y:2022:i:2:d:10.1007_s10589-022-00369-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-022-00369-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/305207","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/305207","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:eref.uni-bayreuth.de:64523","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s10589-022-00369-9","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":{"id":"doi:10.1007/s10589-022-00369-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-022-00369-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00369-9.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2281606148","display_name":null,"funder_award_id":"DFG SPP 1962","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6507445336","display_name":null,"funder_award_id":"SPP 1962","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3147466994.pdf","grobid_xml":"https://content.openalex.org/works/W3147466994.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W581038412","https://openalex.org/W1448623749","https://openalex.org/W1520995709","https://openalex.org/W1566327188","https://openalex.org/W1820125862","https://openalex.org/W1997616626","https://openalex.org/W2008826141","https://openalex.org/W2011655966","https://openalex.org/W2026365342","https://openalex.org/W2039050532","https://openalex.org/W2048742402","https://openalex.org/W2059448319","https://openalex.org/W2079482881","https://openalex.org/W2110017196","https://openalex.org/W2137080665","https://openalex.org/W2162870776","https://openalex.org/W2220137601","https://openalex.org/W2249240397","https://openalex.org/W2496722619","https://openalex.org/W2558210108","https://openalex.org/W2749751111","https://openalex.org/W2763081248","https://openalex.org/W2913806414","https://openalex.org/W2949581229","https://openalex.org/W2951948474","https://openalex.org/W2962721705","https://openalex.org/W2962748029","https://openalex.org/W2963173886","https://openalex.org/W2963317653","https://openalex.org/W2963332075","https://openalex.org/W2963573197","https://openalex.org/W2964195092","https://openalex.org/W3101644375","https://openalex.org/W3106001760"],"related_works":["https://openalex.org/W2940405130","https://openalex.org/W2363211409","https://openalex.org/W2376481828","https://openalex.org/W2112641952","https://openalex.org/W2390990501","https://openalex.org/W2035309570","https://openalex.org/W2002792507","https://openalex.org/W2348787543","https://openalex.org/W4226280031","https://openalex.org/W4387602064"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"develop":[2],"a":[3,99],"globalized":[4],"Proximal":[5,69],"Newton":[6,70],"method":[7],"for":[8,67],"composite":[9,26],"and":[10,31,59],"possibly":[11],"non-convex":[12],"minimization":[13],"problems":[14],"in":[15,34,85,103],"Hilbert":[16],"spaces.":[17],"Additionally,":[18],"we":[19,51],"impose":[20],"less":[21],"restrictive":[22],"assumptions":[23],"on":[24],"the":[25,42,46,53,89],"objective":[27,47],"functional":[28],"considering":[29],"differentiability":[30,40],"convexity":[32],"than":[33],"existing":[35],"theory.":[36],"As":[37],"far":[38],"as":[39,76,78],"of":[41,45,55,92],"smooth":[43],"part":[44],"function":[48,104],"is":[49],"concerned,":[50],"introduce":[52],"notion":[54],"second":[56],"order":[57],"semi-smoothness":[58],"discuss":[60],"why":[61],"it":[62],"constitutes":[63],"an":[64],"adequate":[65],"framework":[66],"our":[68,86,93],"method.":[71],"However,":[72],"both":[73],"global":[74],"convergence":[75,90],"well":[77],"local":[79],"acceleration":[80],"still":[81],"pertain":[82],"to":[83],"hold":[84],"scenario.":[87],"Eventually,":[88],"properties":[91],"algorithm":[94],"are":[95],"displayed":[96],"by":[97],"solving":[98],"toy":[100],"model":[101],"problem":[102],"space.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}